a: \(\frac{52}{17}>\frac{51}{17}=3\)

\(3=\frac{121}{41}>\frac{120}{41}\)

Do đó: \(\frac{52}{17}>\frac{120}{41}\)

b: \(\frac34+\frac14:\left(\frac{7}{12}-\frac16\right)\)

\(=\frac34+\frac14:\left(\frac{7}{12}-\frac{2}{12}\right)\)

\(=\frac34+\frac14:\frac{5}{12}\)

\(=\frac34+\frac14\times\frac{12}{5}=\frac34+\frac35=\frac{15}{20}+\frac{12}{20}=\frac{27}{20}\)

c: \(372,463\cdot998+744,926\)

\(=372,463\cdot998+372,463\cdot2\)

\(=372,463\times\left(998+2\right)=372,463\times1000=372463\)

d: Số số hạng trong dãy số 2;4;6;...;100 là:

\(\left(100-2\right):2+1=98:2+1=49+1=50\) (số)

\(2-4+6-8+10-12+\cdots+98-100+102\)

\(=\left(2-4\right)+\left(6-8\right)+\cdots+\left(98-100\right)+102\)

=(-2)+(-2)+...+(-2)+102

\(=-2\cdot\frac{50}{2}+102=-50+102=52\)

e: (y+112)-113=79

=>y+112-113=79

=>y-1=79

=>y=79+1=80

f: \(\frac34-y=\frac12\)

=>\(y=\frac34-\frac12=\frac14\)

g: \(\left(\frac45-2\times y\right)+\frac16=\frac56\)

=>\(\frac45-2\times y=\frac56-\frac16=\frac46=\frac23\)

=>\(2\times y=\frac45-\frac23=\frac{12}{15}-\frac{10}{15}=\frac{2}{15}\)

=>\(y=\frac{2}{15}:2=\frac{1}{15}\)

h: (y+1)+(y+2)+...+(y+50)=1750

=>50y+(1+2+...+50)=1750

=>\(50y+50\times\frac{51}{2}=1750\)

=>50y+1275=1750

=>50y=1750-1275=475

=>\(y=\frac{475}{50}=9,5\)

a: \(\frac{52}{17}>\frac{51}{17}=3\)

\(3=\frac{121}{41}>\frac{120}{41}\)

Do đó: \(\frac{52}{17}>\frac{120}{41}\)

b: \(\frac34+\frac14:\left(\frac{7}{12}-\frac16\right)\)

\(=\frac34+\frac14:\left(\frac{7}{12}-\frac{2}{12}\right)\)

\(=\frac34+\frac14:\frac{5}{12}\)

\(=\frac34+\frac14\times\frac{12}{5}=\frac34+\frac35=\frac{15}{20}+\frac{12}{20}=\frac{27}{20}\)

c: \(372,463\cdot998+744,926\)

\(=372,463\cdot998+372,463\cdot2\)

\(=372,463\times\left(998+2\right)=372,463\times1000=372463\)

d: Số số hạng trong dãy số 2;4;6;...;100 là:

\(\left(100-2\right):2+1=98:2+1=49+1=50\) (số)

\(2-4+6-8+10-12+\cdots+98-100+102\)

\(=\left(2-4\right)+\left(6-8\right)+\cdots+\left(98-100\right)+102\)

=(-2)+(-2)+...+(-2)+102

\(=-2\cdot\frac{50}{2}+102=-50+102=52\)

e: (y+112)-113=79

=>y+112-113=79

=>y-1=79

=>y=79+1=80

f: \(\frac34-y=\frac12\)

=>\(y=\frac34-\frac12=\frac14\)

g: \(\left(\frac45-2\times y\right)+\frac16=\frac56\)

=>\(\frac45-2\times y=\frac56-\frac16=\frac46=\frac23\)

=>\(2\times y=\frac45-\frac23=\frac{12}{15}-\frac{10}{15}=\frac{2}{15}\)

=>\(y=\frac{2}{15}:2=\frac{1}{15}\)

h: (y+1)+(y+2)+...+(y+50)=1750

=>50y+(1+2+...+50)=1750

=>\(50y+50\times\frac{51}{2}=1750\)

=>50y+1275=1750

=>50y=1750-1275=475

=>\(y=\frac{475}{50}=9,5\)

=20/35*31+30/35*41+45/50*41+35/50*57

=5(1/31-1/35+1/35-1/41+1/41-1/50+1/50-1/57)

=5*(1/31-1/57)

=5*26/1767=130/1767

Vì 4x=9y=12z

Chia cả 3 cho 36 ta được

\(\frac{x}{9}=\frac{y}{4}=\frac{z}{3}\)(và x-y-z=10)

Áp dụng tính chất của dãy tỉ số bằng nhau ta có

\(\frac{x}{9}=\frac{y}{4}=\frac{z}{3}=\frac{x-y-z}{9-4-3}=\frac{10}{2}=5\)

=>x=5.9=45

y=5.4=20

z=5.3=15

l don t now

i don't know

I DON'T KNOW TOO!

Toán lớp 5 thôi!

Quy luật khá dễ bạn nghĩ kĩ đi, nếu bí quá thì làm như tính giá trị biểu thức ấy!

Đặt \(\left\{{}\begin{matrix}a=x^2+y^2\\b=xy\end{matrix}\right.\), HPTTT:

\(\left\{{}\begin{matrix}a^2+4b^2=41\\ab=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}100+4b^4=41b^2\left(1\right)\\a=\dfrac{10}{b}\end{matrix}\right.\)

\(\left(1\right)\Leftrightarrow4b^4-16b^2-25b^2+100=0\\ \Leftrightarrow4b^2\left(b^2-4\right)-25\left(b^2-4\right)=0\\ \Leftrightarrow\left(2b-5\right)\left(2b+5\right)\left(b-2\right)\left(b+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}b=-\dfrac{5}{2}\Rightarrow a=-4\\b=\dfrac{5}{2}\Rightarrow a=4\\b=2\Rightarrow a=5\\b=-2\Rightarrow a=-5\end{matrix}\right.\)

Từ đó thay vào r tính